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3. Logarithms eLearn.Punjab

3.5 Application of Laws of Logarithm in
Numerical Calculations

So far we have applied laws of logarithm to simple type of
products, quotients, powers or roots of numbers. We now extend their
application to more difficult examples to verify their effectiveness in
simplification.

Example 1
Show that

Solution

= 7[log 16 - log 15] + 5[log 25 - log 24] + 3[log 81 - log 80]
= 7[log 24 - log (3 x 5)] + 5[log 52 - log (23 x 3)] + 3[log 34 -
log (24 x 5)]
= 7[4 log 2 - log 3 - log 5] + 5[2 log 5 - 3 log 2 - log 3] + 3[4
log 3 - 4 log2 - log 5]
= (28 - 15 - 12) log 2 + (-7 - 5 + 12) log 3 + (-7 + 10 - 3)log 5
= log 2 + 0 + 0 = log 2 = R.H.S.
Example 2
Evaluate:

Solution

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